Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincaré--Lions inequalities

Giovanni Brigati, Gabriel Stoltz, Andi Q. Wang +1

We study the long-time behavior of the underdamped Langevin dynamics, in the case of so-called \emph{weak confinement}. Indeed, any ${\mathrm{L}}^{\infty }$ distribution (in position an…